What is the volume of this object? Drag on the object to rotate it. $3$ $3\sqrt{2}$
Solution: The volume of a prism is the area of the base $\times$ depth. In this object, one of the triangles is the base. We know the area of a triangle is $\frac{1}{2}\ \text{base} \times \text{height}$ Orient the triangle like this, and find the base and height from the object: $3$ $6$ From the object, we find that the base of the triangle is $6$ and the height is $3$ The area of the triangle is then $\frac{1}{2}6 \times 3 = 9$ From the object, we can then find that the depth is $3$ Then, the final volume is $9 \times 3 = 27.$